DAYTON, Ohio (CNN) -- President Bush Thursday called the Iraqi government's move to launch an offensive against Shiite militants in Basra a "bold decision."

President Bush makes remarks Thursday on the Iraq war at the U.S. Air Force Museum in Dayton, Ohio.

Bush also said he will carefully weigh recommendations from his commanders about how the United States should proceed in Iraq when last year's military buildup ends this summer.

In a wide-ranging address about Iraq at the National Museum of the United States Air Force in Dayton, Ohio, the president stressed the integrity of the Baghdad government to take on crime, no matter who might be committing it.

"There is a strong commitment by the central government of Iraq to say that no one is above the law," said Bush, who called the fight against the "militia fighters and criminals" in the southern Iraqi city a "tough battle." Watch Bush call Iraq a "tough war" »

"Prime Minister [Nuri al-]Maliki's bold decision -- and it was a bold decision -- to go after the illegal groups in Basra shows his leadership and his commitment to enforce the law in an evenhanded manner," he said.

"This operation is going to take some time to complete. And the enemy will try to fill the TV screens with violence, but the ultimate result will be this: Terrorists and extremists in Iraq will know they have no place in a free and democratic society."

But Republican Sen. Chuck Hagel Thursday challenged Bush's optimistic view of the war in Iraq, particularly in light of recent fighting between Iraqi government troops and Shiite militias in the south that is spreading into Baghdad.

Three days of fighting in the southern region have left more than 100 Iraqis dead and prompted thousands to demonstrate Thursday in Shiite neighborhoods of the capital against the crackdown launched by al-Maliki.

"The Shia militias have controlled southern Iraq the last three years," Hagel said on CNN's "The Situation Room."

The senator from Nebraska is an outspoken critic of the war in Iraq who has frequently broken ranks with his fellow Republicans on the issue. He announced last year that he would not seek re-election after his second term in the Senate ends this year.

Nearly 30,000 additional U.S. troops were sent to Iraq last year in what was called a "surge." The administration has said upcoming deployments of combat brigades out of the country will return the troop level to near pre-surge numbers by this summer. Watch Bush say the "surge" is working »

Bush, who touted a strategic bilateral partnership being negotiated with Iraq, said he will discuss the next steps in Iraq later in the year with his national security team and Gen. David Petraeus and U.S. Ambassador to Iraq Ryan Crocker.

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They are to testify before Congress in April about the achievements of the surge and what they believe should come next. He said they also will discuss al Qaeda in Iraq, Shiite extremists, the Kurdistan Workers' Party, and the roles of Syria and Iraq.

Bush said he will "carefully consider" recommendations of Petraeus, Crocker, Defense Secretary Robert Gates and other political and military leaders about troop levels.

"As I consider the way forward, I will always remember that the progress in Iraq is real, it's substantive but it is reversible," he said. "So, the principle behind my decision on our troop levels will be ensuring that we succeed in Iraq. As this debate unfolds, I ask people on both sides to keep an open mind and to take a close look at the situation on the ground."

The president called the U.S. work in Iraq "historic," and said there have been clear security gains there and "less visible" economic and political strides.

"This progress isn't glamorous, but it is important," he said.

Bush also said military and political efforts have hurt al Qaeda in Iraq, citing progress in the tribal uprising against the group in the largely Sunni province of Anbar.

He said coalition and Iraqi forces have driven the group out of strongholds and prompted its migration to Mosul.

"Now al Qaeda's concentrated its efforts in the area of Mosul, which is in northern Iraq. And there's going to be tough fighting in Mosul, and in areas around Mosul in the [coming] weeks and months. But we are determined, along with the Iraqis, to make sure al Qaeda meets the same fate there."

Bush also touted the Iraqis' legislative achievements, including a pension law, a revised de-Baathification law, a new budget, an amnesty law and a provincial powers measure that, he said, sets the stage for provincial elections later this year.

"That's an important piece of legislation because it will give Iraqis who boycotted the last provincial election, such as Sunnis in Anbar, a chance to go to the polls and have a voice in their future," he said.E-mail to a friend